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Expansion of Liquids
00 C with a certain volume V above
1. A block of wood is floating on water at
co
m
water level. The temperature of water is slowly raised from 00C to 200C. How
the volume V change with the rise of temperature
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2) V will go decreasing from beginning to the end
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1) V will remain unchanged
3) V will decrease till the temperature of water reaches at 40C and then it will go on
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decreasing.
4) V will increase till the temperature of water reaches to 40C and then it will go on
decreasing
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2. A liquid with coefficient of volume expansion γ is filled in a container of a
material having the coefficient of linear expansion α . If the liquid overflows on
3.
2) γ > 3α
3) γ < 3α
4) γ > 3α 3
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1) γ = 3α
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heating
When a liquid, taken in a long cylindrical vessel of material with linear
coefficient of expansion ' α ', is heated; the level of liquid did not change. The
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volume coefficient of expansion of liquid is
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1) 3α
2) 2α
3) α
4) 4α
4. The surface water in a lake is going to freeze. Now the temperature of water at
the bottom is
1) 274 K
2) 277 K
3) 100 K
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4) 0K
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5. Apparent expansion of a liquid depends upon
(b) Nature of vessel
(c) Temperature rise
(d) Scale of temperature
1) Only (a) is true
2) (a) & (b) are true
3) (a), (b) & (c) are true
4) (a), (b), (c) & (d) are true
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(a) Nature of liquid
6. Match the following.
List - II
a. Apparent Expansion
e. Nature of vessel & Liquid
b. Real Expansion
f. Nature of Liquid
c. γ a
g. Vessel, Liquid & Temperature
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d. γ r
n.
List - I
h. Liquid & Temperature
2) a - f, b - g, c - h, d - e
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1) a - e, b - f, c - g, d - h
3) a - g, b - h, c - e, d - f
4) a - h, b - e, c - f, d – g
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List - I
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7. Match the following.
List - II
e.
m1
1 + γ a ∆t
b. Corrected Barometric height
f.
d1 − d 2
d 2 ( t2 − t1 )
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w
a. Mass of liquid expelled on heating
c. Coefficient of real expansion of a liquid
d. Mass of liquid remaining on heating
g.
γ a m1∆t
1 + γ a ∆t
h. h0 1 − ( γ r − α ) ∆t 
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1) a - g, b - h, c - f, d - e
2) a - h, b - e, c - g, d - h
3) a - e, b - f, c - g, d - h
4) a - f, b - g, c - h, d – e
8. Match the following.
List - I
List - II
e. Liquid level does not change
b. γ g is -ve
f. Liquid level increases continuously
c. γ g = γ r
g. Liquid level decreases
d. γ g > γ r
h. Liquid level first decreases and
then
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a. γ g is +ve & < γ r
increases
3) a - e, b - f, c - g, d - h
9. Match the following.
List - I
2) a - h, b - f, c - e, d - g
4) a - f, b - g, c - h, d – e
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1) a - g, b - e, c - f, d - h
List - II
e. 273K
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a. Temperature of water at the bottom of a lake
f. 277K
c. γ r of water is positive
g. above 277K
d. Temperature of water just below ice layer in a Lake
h. 273K and 277K
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b. γ r of water is -ve between
1) a - g, b - h, c - e, d - f
2) a - h, b - e, c - f, d - g
3) a - e, b - f, c - g, d - h
4) a - f, b - h, c - g, d – e
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10. A): Real expansion of liquid does not depend upon material of container.
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R): Liquids have no definite shape. They acquire the shape of their containers.
1) Both ‘A’ and ‘R’ are true and ‘R’ is the correct explanation of ‘A’.
2) Both ‘A’ and ‘R’ are true and ‘R’ is not the correct explanation of ‘A’.
3) ‘A’ is true and ‘R’ is false.
4) ‘A’ is false and ‘R’ is true.
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11. A): A vessel is filled, with water, up to brim at 40C. It over flows when the
system is cooled are heated.
R): Water has minimum volume at 40C.
1) Both ‘A’ and ‘R’ are true and ‘R’ is the correct explanation of ‘A’.
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2) Both ‘A’ and ‘R’ are true and ‘R’ is not the correct explanation of ‘A’.
3) ‘A’ is true and ‘R’ is false.
4) ‘A’ is false and ‘R’ is true.
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12. A vessel is half filled with a liquid at 0°C. When the vessel is heated to 100°C,
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the liquid occupies 3/4 volume of the vessel. Coefficient of apparent expansion
of the liquid is
1) 0.5/°C
2) 0.05/°C
3) 0.005/°C
4) 0.0005/°C
1)
γR
2)
8
γR
12
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13. γ A of liquid is 7/8 of γ R of liquid. α g of vessel is
3)
γR
4)
24
γR
36
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14. Co-efficient of apparent expansions of a liquid in Gold vessel is G and when
heated in a silver vessel is S. If coefficient of linear expansion of Gold is A,
G + S − 3A
3
2)
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1)
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coefficient of linear expansion of Silver is
G − S + 3A
3
3)
G + S + 3A
3
4)
G−S + A
3
15. A liquid occupies half of a vessel at a particular temperature. The volume of the
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unoccupied part remains constant at all temperatures. If α and γ are the
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coefficients of linear and real expansions of a vessel and liquid, then γ =
1) 3 α
2) 3 α /2
3) 6 α
16. If on heating a liquid through 800C, the mass expelled is
4) 9 α
1
th of mass still
100
remaining, the coefficient of apparent expansion of the liquid is
1) 12.6 ×10−4 / 0 C
2) 0.8 ×10−4 / 0 C
3) 1.25 ×10−5 / 0 C
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4) 1.25 ×10−4 / 0 C
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17. A glass vessel just holds 50gm of a liquid at 00C. If the coefficient of linear
expansion of glass is 8 ×10−6 / 0 C
The mass of the liquid it holds at 800C is
[coefficient of absolute expansion of liquid = 5 ×10−4 / 0 C ]
1) 46 gm
2) 48 gm
3) 51gm
4) 42 gm
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6
7
18. For a liquid when heated in a vessel it is found that γ A = γ R . Coefficient of
1)
γR
2)
21
γR
3)
11
γR
12
4)
γR
n.
linear expansion of the vessel is
14
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19. When a liquid in a glass vessel is heated, its apparent expansion is 10.3 ×10−4 / 0 C .
Same liquid when heated in a metal, its apparent expansion is 10.06 ×10−4 / 0 C .
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The coefficient of linear expansion of the metal is ( α of glass = 9 × 10−6 / 0 C )
1) 51 × 10−6 / 0 C
2) 43 × 10−6 / 0 C
3) 25 × 10−6 / 0 C
4) 17 × 10−6 / 0 C
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20. Two liter glass flask contains some mercury. It is found that at all temperatures
the volume of the air inside the flask remains the same. The volume of the
( α for glass = 9 ×10−6 / o C , for mercury =
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mercury inside the flask is
1.8 ×10−4 / o C )
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1) 1500cc
2) 150cc
3) 3000cc
4) 300cc
21. The co-efficient of real expansion of Hg is 0.18 ×10−3 / 0 C . If the density of Hg at
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00C is 13.6 gm/c.c its density at 2000 C will be
1) 13.3 gm/c.c
2) 13.13 gm/c.c
3) 13.6 gm/c.c
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4) 13 gm/c.c
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22. A mercury thermometer contains 2c.c. of Hg. at 0°C. Distance between 0°C and
100°C marks on the stem is 35cm and diameter of the bore is 0.02cm. γ A of
liquid is
1) 0.000055/°C
2) 0.000066/°C
3) 0.00055/°C
4) 0.000058/°C
mercury at 00C is 13.6 gm/c.c., its density at 573K will be
2) 13.10 gm/c.c
3) 12.95 gm/c.c
4) 12.75 gm/c.c
n.
1) 12.90 gm/c.c
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23. Coefficient of real expansion of mercury is 0.18 ×10−3 / 0 C . If the density of
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24. A Pycnometer weights 40gm when empty and 1040 gm when filled with mercury
at 00C. On heating to 1000C 10 gm of mercury over flows if the coefficient of
real expansion of mercury is 0.0002/0C. The coefficient of cubical expansion of
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glass is
1) 0.00001/ 0 C
2) 0.0003 / 0 C
3) 0.0002 / 0 C
4) 0.0001/ 0 C
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25. When a block of iron floats in mercury at 00 C , a fraction K1 of its volume is
submerged, while at the temperature
600 C , a fraction K 2 is seen to be
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submerged. If the coefficient of volume expansion of iron is γ Fe and that of
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mercury is γ Hg then the ratio
1 + 60γ Fe
1 + 60γ Hg
2)
1 − 60γ Fe
1 + 60γ Hg
3)
1 + 60γ Fe
1 − 60γ Hg
w
w
1)
K1
can be expressed as
K2
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4)
1 + 60γ Hg
1 + 60γ Fe
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Key
2) 2
3) 1
4) 2
5) 4
6) 3
7) 1
8) 2
9) 4
10) 2
11) 1
12) 3
13) 3
14) 2
15) 3
16) 4
17) 2
18) 1
19) 4
20) 4
21) 2
22) 1
23) 1
24) 4
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1) 4
25) 1
n.
Hints
13. rR = ra + 3α g
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1
rR
24
αg =
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1
3α g = rR
8
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3
V
V−
2 = 0.005 /0C
γA = 4
V
×100
2
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V2 − V1
V1 (t2 − t1 )
12. γ A =
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14. rR = rA + 3α g = cons tan t
G + 3 A = S + 3α 1
G + 3A − S
3
w
α1 =
w
15. γ gVg = γ LVL ⇒ 3αV = γ .
V
⇒ γ = 6α
2
1
M2
M1 − M 2
16. γ A =
= 1.25 x 10 -4 /0C
= 100
M 2 (80)
M 2 (t2 − t1 )
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17. rA =
m1 − m2
m2 × 80
5 × 10−4 − 24 × 10−6 =
50 − x
x × 80
6
7
18. γ R = γ a + 3α g ⇒ γ R = γ R + 3α g ⇒ α g =
co
m
x = 48 gm
1
γR
21
n.
19. γ R = γ a + 3α
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γ a g + 3α g = γ a m + 3α m
∴α m =
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10.3 x 10-4 + 27 x 10-6 = 10.06 x 10-4 + 3 α m
0.51×10−4
= 17 ×10−6 / 0 C
3
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20. γ g Vg = γ L VL
27 x 10-6 x2
= 300cc
1.8 x 10−4
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∴ VL =
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27 x 10-6 x 2 = 1.8 x 10-4 VL
d1
1+ γ R ( t2 − t1 )
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21. d 2 =
∴ d2 =
13.6
13.6
=
= 13.13gs / cc
−3
1 + 0.18 × 10 × 200 1.036
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22. γ A =
22 10−4 × 35
= 55 x 10-6 /0C
×
7
2 ×100
23. d =
d0
13.6
= 13.13 gm
=
1 + rt 1 + 18 × 10−5 × 300
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m
=
πρ 2 h
∆V
=
V ∆t
V ∆t
24. γ R = γ a + γ g
n.
x
(1000 − 10 )(100 )
∴ γa =
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γa =
x
( M 1 − x)(t2 − t1 )
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But γ a =
10
⇒ γ g = 0.0001 / °C
(1000 − 10 )(100 )
Vin d B
=
V
dt
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Fraction (F) =
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25. Weight of body = wt of liquid displaced. Vd B g = Vm dl g
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d 
d 
a1 =  B  & a2 =  B 
 dt 0
 d t t



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w
a1  d B   d t   1 + γ Fet   1 + 60γ Fe
=    = 
=
a2  dt 0  d B t  1 + γ Hg t   1 + 60γ Hg
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